CM1 – Actuarial Mathematics
Build Strong Foundations in Financial Mathematics and Life Contingencies
CM1 – Actuarial Mathematics is one of the Core Principles subjects in the actuarial qualification pathway offered by the Institute and Faculty of Actuaries (IFoA), UK, and the Institute of Actuaries of India (IAI).
The subject introduces mathematical techniques used to value financial cash flows, insurance contracts, annuities, loans, bonds and other financial products. It combines financial mathematics, survival models, life contingencies, pricing and reserving techniques, forming an essential foundation for actuarial studies.
CM1 develops the analytical, mathematical and modelling skills required to understand financial obligations, assess insurance liabilities and evaluate long-term financial risks.
Course Structure & Syllabus
CM1 combines theoretical financial mathematics with practical actuarial modelling using Microsoft Excel.
Key Topics Covered:
- Theory of Interest Rates: Time value of money, compound interest, discounting, interest rate conversions, present value calculations and term structure of interest rates.
- Annuities, Loans & Financial Instruments: Annuity calculations, loan repayment schedules, sinking funds, bond valuation, yield calculations and cash flow analysis.
- Equation of Value & Investment Appraisal: Equations of value, project appraisal, duration, convexity, immunisation and asset-liability matching.
- Survival Models & Life Tables: Mortality rates, survival probabilities, life expectancy, life tables and modelling future lifetimes.
- Life Contingencies & Insurance Contracts: Life assurance, life annuities, joint-life and multiple-life models, benefit valuation and premium calculations.
- Pricing & Reserving: Net and gross premiums, prospective and retrospective reserves, policy values and valuation of insurance liabilities.
- Profit Testing & Actuarial Modelling: Profit testing, analysis of surplus, decrement models and practical actuarial applications using Excel.
The CM1 syllabus focuses on mathematical modelling, financial valuation, actuarial calculations and practical problem-solving, developing essential skills in insurance and financial risk management.
Syllabus Topics & Weightages
The CM1 syllabus comprises four principal areas, with the following indicative weightages under the IFoA curriculum:
| Topic |
Weightage |
| Theory of Interest Rates |
25% |
| Equation of Value and Its Applications |
20% |
| Decrement and Multiple-Life Models |
20% |
| Pricing and Reserving |
35% |
| Total |
100% |
These weightages indicate the approximate syllabus coverage. Actual question distribution may vary between examination sittings.
Examination Structure
CM1 consists of two compulsory components: CM1A (Theory) and CM1B (Practical).
Both papers must be attempted during the same examination sitting.
| Particulars |
IAI (India) |
IFoA (UK) |
| Paper A – Theory |
Objective + Descriptive |
Descriptive |
| Paper A Duration |
3 Hours 15 Minutes |
3 Hours 20 Minutes |
| Paper A Weightage |
70% |
70% |
| Paper B – Practical |
Excel-Based |
Excel-Based |
| Paper B Duration |
1 Hour 45 Minutes |
1 Hour 50 Minutes |
| Paper B Weightage |
30% |
30% |
| Examination Mode |
Centre-Based Online |
In-Person at Exam Centres or Remotely Invigilated Online |
Important Examination Guidelines
- Paper A: Tests theoretical concepts, numerical calculations and actuarial problem-solving. IAI includes both objective and descriptive questions, whereas IFoA follows a descriptive examination format.
- Paper B: Assesses practical actuarial modelling and calculations using Microsoft Excel.
- Combined Assessment: Paper A contributes 70% and Paper B contributes 30% towards the final examination score.
- IFoA Examination Mode: Students can indicate their preference to appear either at an authorised examination centre or remotely through online invigilation. Final allocation is subject to availability and IFoA guidelines.
- IAI Examination Mode: Examinations are conducted online at designated examination centres, in accordance with IAI’s current examination arrangements.
- Examination Requirements: Students must follow their respective institute’s guidelines regarding permitted calculators, actuarial tables, software and examination conduct.
Passing Criteria
The passing requirements differ between IAI and IFoA.
| Institute |
Passing Requirements |
| IAI (India) |
Minimum 30% in each paper and 50% aggregate |
| IFoA (UK) |
Combined weighted marks must meet the pass mark determined for the examination sitting |
Important Information:
- Both Paper A and Paper B must be attempted in the same examination session.
- IAI requires candidates to satisfy both the minimum individual paper marks and the overall aggregate requirement.
- IFoA determines the passing mark for each examination sitting and does not require a separate minimum passing mark in each paper.
- If a candidate does not clear CM1, both components must be attempted again in the next chosen examination sitting.
Eligibility Criteria
CM1 is a Core Principles examination suitable for students beginning their actuarial qualification journey.
- Students can pursue CM1 through the IAI or IFoA examination pathway, subject to the respective institute’s eligibility requirements.
- A strong foundation in mathematics and basic financial concepts is recommended.
- No prior actuarial examination pass is required before attempting CM1 under the IFoA pathway.
- Students must fulfil the applicable membership, registration and examination entry requirements of their selected actuarial institute.
Learning Objectives
Studying CM1 develops the ability to:
- Apply financial mathematics to value future cash flows.
- Calculate annuities, loan repayments and bond values.
- Understand mortality, survival models and life contingencies.
- Determine premiums and reserves for life insurance contracts.
- Analyse financial and insurance liabilities.
- Apply actuarial techniques using Microsoft Excel.
- Develop mathematical modelling and financial risk assessment skills.
Practical Applications of CM1
The knowledge gained in CM1 is applicable across several actuarial and financial disciplines:
- Life Insurance: Premium calculation, policy valuation, profitability analysis and reserving.
- Pensions: Valuation of retirement benefits, annuities and long-term pension obligations.
- Banking & Finance: Loan amortisation, interest rate calculations and bond valuation.
- Investment Management: Fixed-income valuation, cash flow analysis and asset-liability management.
- Risk Management: Modelling financial cash flows, insurance obligations and long-term financial liabilities.
CM1 establishes essential mathematical and actuarial knowledge that supports advanced actuarial subjects and professional applications in insurance, pensions, investments and financial services.
Technical Requirements – AEI Learning Application
To access online classes, recorded lectures and digital study resources, students must ensure their devices meet the following minimum technical requirements of the Actuators Educational Institute (AEI) Learning Application.
| Device / Platform |
Minimum Requirement |
| Android |
Android 9.0 or above |
| Windows PC / Laptop |
Windows 10 or above |
| iPhone / iPad (iOS) |
iOS 12.0 or above |
| MacBook / iMac (macOS) |
Apple M1 chip or above with macOS 14 or later |